[Paper Review] Identification of malfunctioning quantum devices

Michalis Skotiniotis, Santiago Llorens+3 more|arXiv (Cornell University)|Aug 8, 2018

Quantum Information and Cryptography1 references4 citations

TL;DR

This paper investigates optimal strategies for identifying malfunctioning quantum devices in a network of N identical devices, focusing on sources, unitary operations, and quantum channels. It shows that global measurements are optimal for state sources, entanglement improves identification for unitary faults, and entanglement with ancillas is essential for rank-3 Pauli and amplitude damping channels—though separable strategies suffice for rank-1 and rank-2 channels and become asymptotically optimal as N grows.

ABSTRACT

We consider the problem of correctly identifying a malfunctioning quantum device that forms part of a network of $N$ such devices, which can be considered as the quantum analogue of classical anomaly detection. In the case where the devices in question are sources assumed to prepare identical quantum pure states, with the faulty source producing a different anomalous pure state, we show that the optimal probability of successful identification requires a global quantum measurement. We also put forth several local measurement strategies -- both adaptive and non-adaptive, that achieve the same optimal probability of success in the limit where the number of devices to be checked are large. In the case where the faulty device performs a known unitary operation we show that the use of entangled probes provides an improvement that even allows perfect identification for values of the unitary parameter that surpass a certain threshold. Finally, if the faulty device implements a known qubit channel we find that the optimal probability for detecting the position of rank-one and rank-two Pauli channels can be achieved by product state inputs and separable measurements for any size of network, whereas for rank-three and general amplitude damping channels optimal identification requires entanglement with N qubit ancillas.

Motivation & Objective

• To develop optimal protocols for identifying the position of a single malfunctioning quantum device in a network of N identical devices.
• To determine whether entanglement or global measurements are necessary for optimal detection across different types of device faults.
• To compare the performance of separable vs. entangled input states and separable vs. global measurements in fault detection.
• To analyze the scaling of detection success probability with network size N for various channel types.
• To establish conditions under which entanglement provides a significant advantage or becomes asymptotically unnecessary.

Proposed method

• Models the position error identification (PEI) task as a quantum state or channel discrimination problem among N possible faulty device positions.
• For source PEI, formulates the optimal success probability as a semi-definite program (SDP) in dual form, minimizing Tr[Γ] subject to Γ ≥ (1/N)ρ_k for all k.
• For channel PEI, optimizes over both input states and measurements, using a seesaw algorithm for numerical optimization.
• Analyzes the amplitude damping channel by decomposing it into Kraus operators K₀ and K₁, and constructs an ancilla-assisted input state |N,m⟩_pa with fixed excitation number to distinguish faulty positions.
• Uses Gram matrix analysis to compute the upper bound on success probability for amplitude damping channels, showing sub-leading improvement with entanglement.
• Derives analytical expressions for the optimal success probability P_S(ℰ_AD, ρ) in the large-N limit, including corrections up to O(N⁻³).

Experimental results

Research questions

• RQ1 Is a global quantum measurement necessary to achieve optimal success probability in identifying a faulty quantum source?
• RQ2 Can entanglement between input probes improve the probability of identifying a faulty unitary device, and if so, under what conditions?
• RQ3 For Pauli and amplitude damping channels, does the optimal identification strategy require entanglement with ancilla systems?
• RQ4 How does the advantage of entanglement in fault detection scale with the size N of the quantum network?
• RQ5 Can separable input states and measurements achieve optimal detection for certain channel types, and if so, which ones?

Key findings

• For quantum state sources producing a known pure state |ϕ⟩ instead of |0⟩, the optimal success probability is achieved only by a global measurement, specifically the square root measurement.
• For unitary faults, entanglement in the input state improves the success probability and enables perfect identification when the rotation angle exceeds a certain threshold.
• For rank-1 and rank-2 Pauli channels, the optimal success probability is achievable using separable input states and separable measurements, regardless of network size.
• For rank-3 Pauli and amplitude damping channels, optimal identification requires entanglement between N input probes and N ancillas, with the improvement over product states being sub-leading in N.
• In the large-N limit, the performance gap between entangled and separable strategies closes, making separable strategies asymptotically optimal for all channel types.
• The optimal success probability for amplitude damping channels is bounded by P_S(ℰ_AD, ρ) ≤ γ + (√(1−γ)(√(1−γ)+1))/(2N) − γ/(4N²) + O(N⁻³), and this bound is achievable with a specific ancilla-assisted input state.